Classification of simple C*-algebras of tracial topological rank zero

Abstract

We give a classification theorem for unital separable simple nuclear C*-algebras with tracial topological rank zero which satisfy the universal coefficient theorem. Let A and B be two such C*-algebras. We prove that A ≅ B if and only if (K0(A), K0(A)+, [1A], K1(A)) ≅ (K0(B), K0(B)+, [1B], K1B)).